Chapter XI.—The Mystical Meanings in the Proportions of Numbers, Geometrical Ratios, and Music.

As then in astronomy we have Abraham
as an instance, so also in arithmetic we have the same
Abraham. “For, hearing that Lot was taken captive, and having
numbered his own servants, born in his house, 318 (τιὴ33343334Gen. xiv. 14. In Greek
numerals.),” he defeats a very great number of the
enemy.

They say, then, that the character representing
300 is, as to shape, the type of the Lord’s sign,33353335 The Lord’s sign is
the cross, whose form is represented by T; Ιη (the other two letters of τιή,
318) are the first two letters of the name Ἰησοῦς
(Jesus). and that the Iota and the Eta indicate
the Saviour’s name; that it was indicated, accordingly, that
Abraham’s domestics were in salvation, who having fled to the
Sign and the Name became lords of the captives, and of the very many
unbelieving nations that followed them.

Now the number 300 is, 3 by 100. Ten is allowed
to be the perfect number. And 8 is the first cube, which is equality in
all the dimensions—length, breadth, depth. “The days of men
shall be,” it is said, “120 (ρκ´) years.”33363336Gen. vi. 3.
And the sum is made up of the numbers from 1 to 15 added together.33373337 The sum of the numbers from
1 to 15 inclusive is 120. And the moon at 15 days is full.

On another principle, 120 is a triangular33383338 “Triangular
numbers are those which can be disposed in a triangle, as 3 ∴,
6, etc, being represented by the formula (x2 + x)/2” (Liddell and
Scott’s Lexicon). Each side of the triangle of courses
contains an equal number of units, the sum of which amounts to
the number. [Elucidation VI.] number, and consists of
the equality33393339 This
number is called equality, because it is composed of eight numbers,
an even number; as fifty-six is called inequality, because it is
composed of seven numbers, an odd number. of the number 64,
[which consists of eight of the odd numbers beginning with unity],33403340 The clause within brackets
has been suggested by Hervetus to complete the sense. the
addition of which (1, 3, 5, 7, 9, 11, 13, 15) in succession generate
squares;33413341 That is,
1+3+5+7+11+13+15=120; and 1+3=4+5=9+7=16+9=25+11=36+13=49+15=64,
giving us the numbers 4, 9, 16, 25, 36, 49, 64, the squares of 2, 3,
4, 5, 6, 7, 8. and of the inequality of the number 56,
consisting of seven of the even numbers beginning with 2 (2, 4, 6,
8, 10, 12, 14), which produce the numbers that are not squares.33423342ἐτερομήκεις,
the product of two unequal factors, i.e., 2+4+6+8+10+12+14=56; and
2+4=6=3 x 2, 6+4=10=5 x 2, and so on.

Again, according to another way of indicating, the
number 120 consists of four numbers—of one triangle, 15; of
another, a square, 25; of a third, a pentagon, 35; and of a fourth,
a hexagon, 45. The 5 is taken according to the same ratio in each mode.
For in triangular numbers, from the unity 5 comes 15; and in squares, 25;
and of those in succession, proportionally. Now 25, which is the number
5 from unity, is said to be the symbol of the Levitical tribe. And the
500number 35 depends also on the
arithmetic, geometric, and harmonic scale of doubles—6, 8, 9,
12; the addition of which makes 35. In these days, the Jews say that
seven months’ children are formed. And the number 45 depends on
the scale of triples—6, 9, 12, 18—the addition of which
makes 45; and similarly, in these days they say that nine months’
children are formed.

Such, then, is the style of the example in
arithmetic. And let the testimony of geometry be the tabernacle that
was constructed, and the ark that was fashioned,—constructed in
most regular proportions, and through divine ideas, by the gift of
understanding, which leads us from things of sense to intellectual
objects, or rather from these to holy things, and to the holy
of holies. For the squares of wood indicate that the square form,
producing right angles, pervades all, and points out security. And the
length of the structure was three hundred cubits, and the breadth fifty,
and the height thirty; and above, the ark ends in a cubit, narrowing to
a cubit from the broad base like a pyramid, the symbol of those who are
purified and tested by fire. And this geometrical proportion has a place,
for the transport of those holy abodes, whose differences are indicated
by the differences of the numbers set down below.

And the numbers introduced are sixfold, as three
hundred is six times fifty; and tenfold, as three hundred is ten times
thirty; and containing one and two-thirds (επιδίμοιροι),
for fifty is one and two-thirds of thirty.

Now there are some who say that three hundred cubits
are the symbol of the Lord’s sign;33433343 The cross. and fifty, of hope and of the
remission given at Pentecost; and thirty, or as in some, twelve, they say
points out the preaching [of the Gospel]; because the Lord preached in His thirtieth year; and
the apostles were twelve. And the structure’s terminating in a
cubit is the symbol of the advancement of the righteous to oneness and
to “the unity of the faith.”33443344Eph. iv.13.

And the table which was in the temple was six
cubits;33453345Ex. xxv. 23. The
table is said to be two cubits in length, a cubit in breadth, and a
cubit and a half in height; therefore it was six cubits round.
and its four feet were about a cubit and a half.

They add, then, the twelve cubits, agreeably
to the revolution of the twelve months, in the annual circle, during
which the earth produces and matures all things; adapting itself to
the four seasons. And the table, in my opinion, exhibits the image of
the earth, supported as it is on four feet, summer, autumn, spring,
winter, by which the year travels. Wherefore also it is said that
the table has “wavy chains;”33463346Ex. xxv. 24. either because the universe
revolves in the circuits of the times, or perhaps it indicated the earth
surrounded with ocean’s tide.

Further, as an example of music, let us
adduce David, playing at once and prophesying, melodiously praising
God. Now the Enarmonic33473347
The three styles of Greek music were the ἐναρμονικόν,
διάτονον,
and χρωματικόν.
suits best the Dorian harmony, and the Diatonic the Phrygian, as
Aristoxenus says. The harmony, therefore, of the Barbarian psaltery,
which exhibited gravity of strain, being the most ancient, most certainly
became a model for Terpander, for the Dorian harmony, who sings the
praise of Zeus thus:—

“O Zeus, of all things the Beginning, Ruler of all;

O Zeus, I send thee this beginning of hymns.”

The lyre, according to its primary
signification, may by the psalmist be used figuratively for the Lord;
according to its secondary, for those who continually strike the chords
of their souls under the direction of the Choir-master, the Lord. And
if the people saved be called the lyre, it will be understood to be in
consequence of their giving glory musically, through the inspiration
of the Word and the knowledge of God, being struck by the Word so as to
produce faith. You may take music in another way, as the ecclesiastical
symphony at once of the law and the prophets, and the apostles along
with the Gospel, and the harmony which obtained in each prophet, in the
transitions of the persons.

But, as seems, the most of those who are inscribed
with the Name,33483348 i.e.,
of Christ. like the companions of Ulysses, handle the word
unskilfully, passing by not the Sirens, but the rhythm and the melody,
stopping their ears with ignorance; since they know that, after lending
their ears to Hellenic studies, they will never subsequently be able to
retrace their steps.

But he who culls what is useful for the advantage
of the catechumens, and especially when they are Greeks (and the earth
is the Lord’s, and the fulness thereof334933491 Cor. x. 26, etc.), must not abstain from
erudition, like irrational animals; but he must collect as many aids
as possible for his hearers. But he must by no means linger over these
studies, except solely for the advantage accruing from them; so that,
on grasping and obtaining this, he may be able to take his departure
home to the true philosophy, which is a strong cable for the soul,
providing security from everything.

Music is then to be handled for the sake
of the embellishment and composure of manners. For instance,
at a banquet we pledge each other while the music is playing;33503350ψάλλοντες
is substituted by Lowth for ψάλλειν of
the text; ἐν
τῷ ψάλλειν has also
been proposed. soothing by song the eagerness of our desires,
and glorifying God
501for the copious gift of human
enjoyments, for His perpetual supply of the food necessary for the growth
of the body and of the soul. But we must reject superfluous music, which
enervates men’s souls, and leads to variety,—now mournful,
and then licentious and voluptuous, and then frenzied and frantic.

The same holds also of astronomy. For treating
of the description of the celestial objects, about the form of the
universe, and the revolution of the heavens, and the motion of the stars,
leading the soul nearer to the creative power, it teaches to quickness
in perceiving the seasons of the year, the changes of the air, and the
appearance of the stars; since also navigation and husbandry derive
from this much benefit, as architecture and building from geometry.
This branch of learning, too, makes the soul in the highest degree
observant, capable of perceiving the true and detecting the false,
of discovering correspondences and proportions, so as to hunt out for
similarity in things dissimilar; and conducts us to the discovery of
length without breadth, and superficial extent without thickness, and
an indivisible point, and transports to intellectual objects from those
of sense.

The studies of philosophy, therefore, and philosophy
itself, are aids in treating of the truth. For instance, the cloak
was once a fleece; then it was shorn, and became warp and woof; and
then it was woven. Accordingly the soul must be prepared and variously
exercised, if it would become in the highest degree good. For there is
the scientific and the practical element in truth; and the latter flows
from the speculative; and there is need of great practice, and exercise,
and experience.

But in speculation, one element relates to
one’s neighbours and another to one’s self. Wherefore also
training ought to be so moulded as to be adapted to both. He, then, who
has acquired a competent acquaintance with the subjects which embrace
the principles which conduce to scientific knowledge (gnosis),
may stop and remain for the future in quiet, directing his actions in
conformity with his theory.

But for the benefit of one’s neighbours,
in the case of those who have proclivities for writing, and those who
set themselves to deliver the word, both is other culture beneficial,
and the reading of the Scriptures of the Lord is necessary, in order to
the demonstration of what is said, and especially if those who hear are
accessions from Hellenic culture.

Such David describes the Church: “The
queen stood on thy right hand, enveloped in a golden robe,
variegated;”33513351Ps. xlv. 9. and with Hellenic and superabundant
accomplishments, “clothed variegated with gold-fringed
garments.”33523352Ps. xlv. 14. [Elucidation VII.] And the Truth says by the
Lord, “For who had known Thy counsel, hadst Thou not given wisdom,
and sent Thy Holy Spirit from the Highest; and so the ways of those on
earth were corrected, and men learned Thy decrees, and were saved by
wisdom?” For the Gnostic knows things ancient by the Scripture,
and conjectures things future: he understands the involutions of words
and the solutions of enigmas. He knows beforehand signs and wonders,
and the issues of seasons and periods, as we have said already. Seest
thou the fountain of instructions that takes its rise from wisdom? But
to those who object, What use is there in knowing the causes of the
manner of the sun’s motion, for example, and the rest of the
heavenly bodies, or in having studied the theorems of geometry or
logic, and each of the other branches of study?—for these
are of no service in the discharge of duties, and the Hellenic
philosophy is human wisdom, for it is incapable of teaching33533353διδακτικήν,
proposed by Sylburgius, seems greatly preferable to
the reading of the text, διδακτήν,
and has been adopted above. the truth—the following
remarks are to be made. First, that they stumble in reference to the
highest of things—namely, the mind’s free choice. “For
they,” it is said, “who keep holy holy things, shall be made
holy; and those who have been taught will find an answer.”33543354Wisd. vi. 10.
For the Gnostic alone will do holily, in accordance with reason all that
has to be done, as he hath learned through the Lord’s teaching,
received through men.

Again, on the other hand, we may hear: “For
in His hand, that is, in His power and wisdom, are both we and our
words, and all wisdom and skill in works; for God loves nothing but
the man that dwells with wisdom.”33553355Wisd. vii. 16. And again, they have not
read what is said by Solomon; for, treating of the construction of the
temple, he says expressly, “And it was Wisdom as artificer that
framed it; and Thy providence, O Father, governs throughout.”33563356Wisd. xiv. 2, 3.
And how irrational, to regard philosophy as inferior to architecture and
shipbuilding! And the Lord fed the multitude of those that reclined on the
grass opposite to Tiberias with the two fishes and the five barley loaves,
indicating the preparatory training of the Greeks and Jews previous to
the divine grain, which is the food cultivated by the law. For barley
is sooner ripe for the harvest than wheat; and the fishes signified
the Hellenic philosophy that was produced and moved in the midst of the
Gentile billow, given, as they were, for copious food to those lying on
the ground, increasing no more, like the fragments of the
502loaves, but having partaken of
the Lord’s blessing, and breathed into them the resurrection
of Godhead33573357 That is,
resurrection effected by divine power. through the power of the
Word. But if you are curious, understand one of the fishes to mean the
curriculum of study, and the other the philosophy which supervenes. The
gatherings33583358 Such
seems the only sense possible of this clause,—obtained,
however, by substituting for συνάλογοι
λόγοὐ κ.τ.λ.,
σύλλογοι
λόγον κ.τ.λ.
point out the word of the Lord.

“And the choir of mute fishes rushed to it,”

says the Tragic Muse
somewhere.

“I must decrease,” said the prophet John,33593359John iii. 30.
and the Word of the Lord alone, in which the law terminates,
“increase.” Understand now for me the mystery of the truth,
granting pardon if I shrink from advancing further in the treatment of
it, by announcing this alone: “All things were made by Him, and
without Him was not even one thing.”33603360John i. 3. Certainly He is called
“the chief corner stone; in whom the whole building, fitly
joined together, groweth into an holy temple of God,”33613361Eph. ii. 20, 21.
according to the divine apostle.

I pass over in silence at present the parable
which says in the Gospel: “The kingdom of heaven is like a man who
cast a net into the sea and out of the multitude of the fishes caught,
makes a selection of the better ones.”33623362Matt. xiii. 47, 48.

And now the wisdom which we possess announces
the four virtues33633363
Prudence, fortitude, justice, temperance. [Known as the philosophical
virtues.] in such a way as to show that the sources of them
were communicated by the Hebrews to the Greeks. This may be learned
from the following: “And if one loves justice, its toils are
virtues. For temperance and prudence teach justice and fortitude; and
than these there is nothing more useful in life to men.”

Above all, this ought to be known, that by nature
we are adapted for virtue; not so as to be possessed of it from our birth,
but so as to be adapted for acquiring it.

3338 “Triangular
numbers are those which can be disposed in a triangle, as 3 ∴,
6, etc, being represented by the formula (x2 + x)/2” (Liddell and
Scott’s Lexicon). Each side of the triangle of courses
contains an equal number of units, the sum of which amounts to
the number. [Elucidation VI.]

3339 This
number is called equality, because it is composed of eight numbers,
an even number; as fifty-six is called inequality, because it is
composed of seven numbers, an odd number.

3340 The clause within brackets
has been suggested by Hervetus to complete the sense.